This article presents a formal explanation of the forecast combination puzzle, that simple combinations of point forecasts are repeatedly found to outperform sophisticated weighted combinations in empirical applications. The explanation lies in the effect of finite-sample error in estimating the combining weights. A small Monte Carlo study and a reappraisal of an empirical study by Stock and Watson ["Federal Reserve Bank of Richmond Economic Quarterly" (2003) Vol. 89/3, pp. 71-90] support this explanation. The Monte Carlo evidence, together with a large-sample approximation to the variance of the combining weight, also supports the popular recommendation to ignore forecast error covariances in estimating the weight. Copyright (c) Blackwell Publishing Ltd and the Department of Economics, University of Oxford, 2009.

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The finite mixture distribution is proposed as an appropriate statistical model for a combined density forecast. Its implications for measures of uncertainty and disagreement, and for combining interval forecasts, are described. Related proposals in the literature and applications to the U.S. Survey of Professional Forecasters are discussed.

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